A Note on Core Regions of Membership Functions

In neuro-fuzzy approaches different membership functions are used for modeling the system's rule set. Two wellknown membership function types are triangle functions and trapezoid functions. In our contribution we demonstrate that trapezoid functions with larger core regions are the more appropriate functions for calculating the membership degrees within neuro-fuzzy systems. If regions of the data of different classes are highly overlapping or if the data is noisy, the values of the membership degrees could be misleading with respect to rule confidence if the core region is modeled too small. In fact, we show that data regions with a high membership degree need not to be the regions with a high rule confidence. This effect that we call membership unrobustness is discussed. We give preliminary benchmark examples and show how this effect influenced our recent work of analysing septic shock patient data.